Offensive and honest, but not loud (4)
I believe the answer is:
rank
'offensive' is the definition.
('rank' can be similar in meaning to 'offensive')
'honest but not loud' is the wordplay.
'honest' becomes 'frank' ('frank' can be similar in meaning to 'honest').
'but not' suggests deleting specific letters.
'loud' becomes 'f' (A musical term).
'frank' with 'f' taken away is 'RANK'.
'and' is the link.
(Other definitions for rank that I've seen before include "Highly disagreeable" , "Relative status" , "Status; foul" , "Classify" , "A tax stand" .)